Question

Suppose a customer’s house increased in value over five years from $150,000 to $250,000. What was the annual growth rate of the property value during this five- year interval? Three local banks pay different interest rates on time deposits with one-year maturities. Rank the three banks from highest to lowest in terms of the depositor’s return.

Bank 1—4.5 percent per year compounded annually

Bank 2—4.3 percent per year compounded quarterly

Bank 3—4.1 percent per year compounded daily

Answer 1

Calculation of the annual growth rate of the property value during this five- year interval
Future Value = Present Value x (1+Annual growth rate)^Number of years
250000 = 150000 x (1+Annual Growth rate)^5
1.67 = (1+Annual growth rate)^5
Annual growth rate = 10.80%
Calculation of effective annual return on deposits
Effective annual return = (1+r)^n -1
r = interest rate per compounding period and n = number of compounding periods in a year
Effective annual return for Bank 1 deposit = (1+0.045)^1 - 1 = 4.50%
Effective annual return for Bank 2 deposit = (1+0.043/4)^4 - 1 = 4.37%
Effective annual return for Bank 3 deposit = (1+0.041/365)^365 - 1 = 4.18%
Ranking of the three banks from highest to lowest in terms of the depositor’s return.
Rank	Return %	Bank
1	4.50%	Bank 1
2	4.37%	Bank 2
3	4.18%	Bank 3